摘要
文章以p-群和内∑-群研究成果为基础,以它们的研究方法为依托,采用反证法、分析法,得到若干成果,丰富了研究内∑-群这一领域的成果。文章首先以可解次单群的结构和性质,引出所讨论的任一真子群为素数方幂阶的有限群的结构和性质,给出一个有限群满足这一性质的充分必要条件,得到了若干结论,并且指出了任一真子群为素数方幂阶的有限群和有限次单群、CP-群之间的包含关系。最后,进一步拓宽这一性质,引出外p-群的定义,给出了一个外p-群的必要条件。
To study the results based on p-groups and inner ∑-groups, and their research methods, with the methods of reversed proof and analysis proof, the paper first uses the quality and structure of the sub-simplegroups to give the quality and structure of the finite groups with many subgroups of prime power order and necessary and sufficient condition. In addition to pointing out the relationship of the finite groups with many subgroups of prime power order, sub-simplegroups and CP-groups. At last, the external p-groups and the condition of this groups is given.
出处
《四川理工学院学报（自然科学版）》
CAS
2010年第1期25-27,共3页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
关键词
次单群
P-群
内p-群
IP-群
sub-simple groups
p-groups
inner p-groups
IP-groups
